Structural investigation of silicon nanowires using GIXD and GISAXS: Evidence
of complex saw-tooth faceting
Thomas David
*
, Denis Buttard, Tobias Schülli, Florian Dallhuin, Pascal Gentile
CEA/GRENOBLE-INAC/SP2M/SiNaPS, 17 rue des Martyrs, 38054 Grenoble Cedex 9, France
article info
Article history:
Received 21 March 2008
Accepted for publication 24 June 2008
Available online 2 July 2008
Keywords:
X-ray scattering
Diffraction
GIXD
GISAXS
Epitaxy
Silicon
Nanowire
Facet
abstract
We present the results of X-ray experiments on silicon nanowires grown on h111i-oriented silicon sub-
strate using the vapor liquid solid method. Grazing incidence X-ray diffraction shows that nanowires are
in epitaxy on the substrate and have a hexagonal cross-section. The orientations of the sides are then
determined. Grazing incidence small-angle X-ray scattering experiments reveal fine saw-tooth faceting
of the sides of the nanowires. This fine saw-tooth faceting appears with alternating upward and down-
ward orientations on each side of the nanowires, reflecting the trigonal symmetry of the nanowires.
The crystallographic orientation of some of these facets is then determined. Finally, it is observed that
large-diameter nanowires (diame ter larger than 200 nm) exhibit six additional faces that truncate the
edge of the usual hexagonal cross-section of the nanowires. These additional faces also show saw-tooth
faceting which is tilted with respect to the horizontal and seems to be present only around the top of the

small-angle X-ray scattering (GISAXS) has already proved its effi-
ciency in the study of silicon nanocrystals [7]. We performed
grazing incidence X-ray diffraction (GIXD) and GISAXS experi-
ments on ‘big’ silicon nanowires (diameters from 50 to 500 nm)
grown by VLS on h111i-oriented silicon substrate with a gold cat-
alyst. Crystal orientation and structural properties of the nano-
wires were deduced from GIXD while GISAXS provided
information about the shape of the nanowires, their faceting
and the orientation of their facets.
2. Experimental details
2.1. Nanowire growth
Nanowires were grown on a h111i oriented silicon substrate.
The catalysts used in the VLS reaction were gold droplets dewetted
from a thin evaporated film ($ 2 nm thick). The growth took place
0039-6028/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.susc.2008.06.022
* Corresponding author. Tel.: +33 4 38 78 31 12; fax: +33 4 38 78 58 17.
E-mail address: [email protected] (T. David).
Surface Science 602 (2008) 2675–2680
Contents lists available at ScienceDirect
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journal homepage: www.elsevier.com/locate/susc
in a chemical vapor deposition (CVD) reactor, at 20 mbar and
around 600 °C. The gazeous precursor was silane whereas the car-
rier gas was hydrogen. For additional details about controlled VLS
growth of silicon nanowires see [8]. After growth, scanning elec-
tron microscopy (SEM) images of the resulting nanowires were
produced (Fig. 1) and showed h111i oriented nanowires perpendic-
ular to the surface of the substrate. Their diameters were not con-
trolled because the diameters of the droplets obtained from the

gle
a
e
with respect to the sample surface remains small and com-
parable to
a
i
while the scattering angle 2d in the plane of the
sample surface can be large. In GISAXS, both emergent and scatter-
ing angles are small, and images of the scattered intensity are re-
corded just around the direct beam and specular reflection. For
GIXD, a position sensitive detector (PSD) was used while for GI-
SAXS a 1152 Â 1242 pixels low-noise 16-bit CCD detector from
Princeton was used.
3. Results
3.1. GIXD: Shape and epitaxial orientation of the nanowires
Fig. 3a shows a profile of the diffracted intensity around the
ð2

20Þ reflection. We observe two diffraction peaks, the narrower
(S) coming from the substrate and the broader (NW) from the wires,
indicating that nanowires are single crystals and that their in-plane
orientation is the same as the one of the substrate. Using Bragg’s
law 2d sinh ¼ k for the selected wavelength k = 0.10619 nm we
can estimate the lattice parameter a
Si
and a
nw
, respectively, of the
substrate and the nanowires. We then deduce the lattice mismatch

1; ½2

1

1; ½11

2; ½1

21 and ½

211. Similarly, the directions
of the edges between two faces are ½1

10 and the five other equiv-
alent directions. These results are consistent with previous elec-
tronic microscopy observations [10]. As this map shows the
scattered intensity coming from the entire population of nano-
wires illuminated by the beam, we can be sure that these nano-
wires are all in epitaxy with the substrate and have the same in-
plane orientation. Otherwise the map would show an arc following
a Debye–Scherrer ring.
The same experiment was performed on another sample ob-
tained after a shorter period of growth, resulting in nanowires at
the very beginning of their growth. The corresponding map (not
shown) has a round shape without streaks, showing that the hexa-
gon faces have not yet been formed.
3.2. GISAXS: fine saw-tooth faceting
Fig. 4a shows a GISAXS image obtained with the incident beam
along the ½1


e
are, respectively the incident and
emergent wave vector. The scattering vector is
~
q ¼
~
k
e
À
~
k
i
with q ¼
4
p
k
sinðhÞ.
2676 T. David et al. / Surface Science 602 (2008) 2675–2680
hexagonal cross-section of the wires shown earlier. These rods are
produced by supplementary facets on the principal faces. This is
consistent with the saw-tooth faceting observed earlier [5,10].By
measuring the tilt angle we can estimate the orientation of the
facets.
Finally, on all GISAXS measurements, and especially in Fig. 4a, a
splitting of the scattered streak may be observed. This phenome-
non is due to multiple scattering effects and has already been
investigated [11–15].
The diffuse streaks produced by facets are schematically repre-
sented in Fig. 5. The incident X-ray beam is scattered by facets and
the scattering vector

a
R
¼
a
M
Þ. But if
u
6¼ 0

;
~
q
xy
and
~
q are out of the CCD plane and a
correction is needed as tanð
a
R
Þ¼tanð
a
M
Þ= cosð
u
Þ. It is important
to note that the visibility of streaks on the GISAXS image decreases
quickly when
u
increases. Facet indexation with the corrected an-
gle is analysed in Section 4.

M
ÞÀa
M
and u are defined in Fig. 5. In image (a) asymmetry between the left and
right is noticeable, while image (b) is symmetrical. Intensity is given in a logarithmic scale. Inserts: schematic top view of a nanowire cross-section.
T. David et al. / Surface Science 602 (2008) 2675–2680
2677
tions of Ross et al. in [5] which show that only one out of two sides
are saw-tooth faceted. However, as shown in Fig. 1b–e, our SEM
observations are not very consistent with the simple faceting mod-
el usually proposed. Indeed, we observe saw-tooth faceting on each
side of the nanowire. For large-diameter wires (i.e. diameter larger
than 200 nm) the hexagonal cross-section is replaced by a dodec-
agonal section. It seems that the six additional faces are wider at
the top (Fig. 1c), while almost non-existent at the bottom (Fig. 1d).
All these observations lead us to reconsider the nanowire facet
model and to propose a new one, as shown in Fig. 6.InFig. 6awe
can observe the dodecagonal section. The twelve faces are all saw-
tooth faceted and distributed in three families. The (LF) family cor-
responds to large upward-oriented facets as indicated in Fig. 6b
and the (SF) family corresponds to small upward-oriented facets.
The two opposite faces are centrosymetric. This is the reason
why the GISAXS image in Fig. 4a is asymmetric. This is perfectly
consistent with the trigonal character of the nanowires. For large
diameter nanowires (diameter larger than 200 nm), six additional
faces appear as a result of the truncation of the hexagon edge, pro-
ducing the (TF) family corresponding to tilted saw-tooth faceting.
The GISAXS image is consistent with this explanation, as shown
in Fig. 7. On the GISAXS image in Fig. 7, the ‘large’ facets produce a
streak at 10

rection explained earlier. In the same way, the ‘small’ facets would
produce streaks at 19.5° (intense) and 37° (weak). Combining the
two, we have one superimposed streak at 19.5° on the left of the
image and two distinct streaks at 10° and 37° on the right. As
the streak at 37° corresponds to a diffraction vector outside the
detector plane ð
u
6¼ 0

Þ, its intensity is very weak compared to
the two other at 10° and 19.5°. This is exactly what we observe
in Figs. 4a and 7 with an acceptable error of 1°. The SEM image
in Fig. 1 corresponds well with this explanation since we measure
an angle of about 9.5° with respect to the vertical for the large fac-
ets and 20° for the small ones. It is interesting to note that the an-
gles determined locally by Ross et al. in [5] using SEM measure
11.2° and 23.3° values, which are close to ours. Similar results have
also been reported with TEM observations [10]. In terms of direc-
tion, the facets tilted at 19.5° correspond to ð

1

11Þ planes and those
tilted at 10° correspond to ð

1

13Þ planes.
Finally, we must explain the existence of the diffuse streaks at
approximately 60° in Fig. 4a and at approximately 34° in Fig. 4b.

image is asymmetric. (For interpretation of the references to colour in this figure
legend, the reader is referred to the web version of this article.)
Fig. 7. Correspondence between the streaks visible on the GISAXS image and the
different types of faces. The two streaks marked with black solid lines correspond to
the facets whose normal is in the detector plane ð
u ¼ 0

Þ. These facets are present
on two of the faces of types (LF) and (SF). The two streaks marked with large blue
dashed lines correspond to the same facets but with
u 6¼ 0

, present on the other
faces of type (LF) and (SF). Finally, the two streaks marked with small red dashed
lines probably correspond to the other tilted facets present on the faces of type (TF).
These faces are only present on nanowires whose diameters are larger than 200 nm.
The intensity is given in a logarithmic scale. (For interpretation of the references to
colour in this figure legend, the reader is referred to the web version of this article.)
2678 T. David et al. / Surface Science 602 (2008) 2675–2680
4.2. Other results concerning silicon faceting
Numerous theoretical articles have already been published on
this topic. These have usually demonstrated that the orientation
of these facets strongly depends on growth conditions and espe-
cially on temperature. Thus Bermond et al. [18] conducted experi-
mental observations of silicon nanowhisker faceting at different
temperatures. The results show facets of type {1 1 3}, {110},
{100} and {111} after annealing at T > 1000 K. The authors provide
evidence that these facets depend on surface tension
c
. They show

, which is non-conventional.
On the other hand, Zhang et al. [19] carried out calculations for
structures and energetics for hydrogen-terminated silicon nano-
wire surfaces that produced more classical results. The h112i sili-
con nanowires with only two {1 1 1} and two {110} surfaces
appear to be more energetically favorable than the h110i wire sur-
rounded by four {1 1 1} surfaces. In the case of h111i nanowires, dif-
ferent faceting is possible, leading to different cross-sections such
as triangular, truncated triangular or hexagonal. The stability of sil-
icon nanowires is determined by competition between the minimi-
zation of surface energy of facets
c
111
<
c
110
<
c
100
, in inverse
proportion to the surface atomic density of these facets, and the
minimization of the surface-to-volume ratio svr ðsvr
hexag:
>
svr
rectangular
> svr
triang:
Þ.
Important among the theoritical studies is the article by Rurali

and Ross et al. [5] with saw-tooth faceting. They interpret this fac-
eting term of both the role of the geometry and surface energy of
the wire and the liquid droplet, and report that the period and
amplitude of saw-tooth faceting are directly proportional to wire
diameter. However, the origin of the facets presented in the litera-
ture is not really explained or understood, even if it is clear that the
gold catalyst plays a key role.
4.3. Why these facets in our experiments?
As briefly shown above, surface faceting mechanisms have been
attracting attention for years. See [28] for instance, for a general
explanation of parameters determining stable facets. With regard
to bulk silicon, many groups have studied different types of facet-
ing, especially in the presence of gold on the surface, and mostly
using self-organised systems [29–31]. Most stable facet orienta-
tions in all these studies appear to depend on the gold covering
of the silicon surface but h111i and h113i directions seem to be
particularly stable, corroborating our results. Thus, each natural
ð

1

12Þ side of our nanowires would show ð

1

11Þ and ð

1

13Þ facets.

12i directions.
We determined the direction of small saw-tooth facets (ð

1

11Þ
and ð

1

13Þ) and found that this saw-tooth faceting appeared on
every side of the nanowires rather than on one of the two sides.
However, the faceting proved to be head-to-tail on half of the sides,
thus confirming the trigonal symmetry of the nanowires. As X-rays
show the average signal from the nanowires over the whole sam-
ple, all these properties are visible only because of the overall
homogeneity.
Finally, we observed a change in cross-section from hexagonal
to dodecagonal near the top of the large nanowires. The new sides
also seem to be saw-tooth faceted but with another kind of facet.
The relative stability of these other facets compared with the
‘usual’ ones might be the result of a different level of surface gold
coverage near the catalyst.
Acknowledgements
This work has been carried out as part of the PREEANS ANR pro-
ject. We are sincerely grateful to T. Baron and P. Ferret for their
fruitful discussions.
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